"Marriage defenders" rarely go into much, or even any, detail demonstrating how specifically all men are different from all women from a psychological standpoint, of course. However, the above summary is the basic gist of the argumentation.
Extending this ideology further, many ladies very quickly learn that being "complementary" to men means being less-than men. Whenever a human difference is exaggerated to the extent that the sex/gender one has been, you can pretty much guarantee that some sort of hierarchy is also involved. The "truth" about women, often deriving from Christian and other male supremacist religious traditions, is that we are some sort of inferior version of men. Unlike men, who are natural leaders created in the very image of god "himself," women are alleged natural born submissives created from that rather insubstantial part of man, his rib.
The truth threat of same-sex marriage is that it knocks this ideology right on its outdated, artificial ass. To recognize same-sex marriage as a legitimate institution recognizes that while sex and gender are different categories, they are not as important and hierarchical as "common sense" dictates.
When I read through this article in The New York Times regarding research on same-sex parenting, which I first saw at PF's place, I was reminded of this once more. For much of the history of LGBT advocacy, those opposed to LGBT rights relied on their "common sense" to warn that children of gay people would turn out gay, crazy, confused, molested, and generally just Really Bad Off. Appealing to pathos by using baby talk and images of cherubic children, they appeal to the "common sense" of like-minded Americans by repeating over and over again like wacky parrots that All Kids Need a Mommy and a Daddy.
What the accumulated research shows, as noted in the NYT article, is that "children of same-sex parents are not markedly different from those of heterosexual parents." And, as journalist Lisa Belkin notes, the differences that are observed are quite interesting:
"There are data that show, for instance, that daughters of lesbian mothers are more likely to aspire to professions that are traditionally considered male, like doctors or lawyers — 52 percent in one study said that was their goal, compared with 21 percent of daughters of heterosexual mothers, who are still more likely to say they want to be nurses or teachers when they grow up. (The same study found that 95 percent of boys from both types of families choose the more masculine jobs.) Girls raised by lesbians are also more likely to engage in “roughhousing” and to play with “male-gendered-type toys” than girls raised by straight mothers. And adult children of gay parents appear more likely than the average adult to work in the fields of social justice and to have more gay friends in their social mix."
Not only does the legalization of same-sex marriage send the message that marriage can exist without the socially constructed sex/gender hierarchy, it also knicks away at the prison of sex/gender roles. It is perhaps the most obvious message society can send to women that they can be something other than subservient wife to a man, and to men, that they can be something other than head of household over a woman and children. Yes, not all heterosexuals experience marriage in so traditional of terms, but same-sex marriage legitimizes the message that marriage- and those within it- are and can be something else.
It makes sense that girls of same-sex parents would listen to that message. One researcher quoted at the end of the article notes that taking gender out of the equation offers more role fluidity to same-sex partnerships than heterosexual ones. Perhaps it does more than that. Perhaps it allows girl children of such partnerships to be more than pink little girls. It shows them how to be a little bit more human.